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Article overview
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Threefold symmetric Hahn-classical multiple orthogonal polynomials | | Ana F. Loureiro
; Walter Van Assche
; | | Date: |
27 Dec 2018 | | Abstract: | We characterize all the multiple orthogonal threefold symmetric polynomial
sequences whose sequence of derivatives is also multiple orthogonal. Such a
property is commonly called the Hahn property and it is an extension of the
concept of classical polynomials to the context of multiple orthogonality. The
emphasis is on the polynomials whose indices lie on the step line, also known
as $2$-orthogonal polynomials. We explain the relation of the asymptotic
behavior of the recurrence coefficients to that of the largest zero (in
absolute value) of the polynomial set. We provide a full characterization of
the Hahn-classical orthogonality measures supported on a $3$-star in the
complex plane containing all the zeros of the polynomials. There are
essentially three distinct families, one of them $2$-orthogonal with respect to
two confluent functions of the second kind. This paper complements earlier
research of Douak and Maroni. | | Source: | arXiv, 1901.1121 | | Services: | Forum | Review | PDF | Favorites | |
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